The flexure hinge is one of the important components of fast steering mirror (FSM). The impact of its structural characteristic on FSM performance was analyzed to guide the structure design of FSM. The flexure hinge was simplified as an elastic joint, which could be equivalent to triaxial translational stiffness and triaxial rotational stiffness. Based on the Euler dynamics theory, the motion differential equation of a two-axis FSM was derived, and the Simulink model of the FSM control system was established. Under the given vibration condition, the influence of structural resonant frequency on FSM performance was simulated. The results showed that the higher the translational resonant frequency, the higher the FSM lock zero accuracy, and the translational resonant frequency should be more than two times of the gain crossover frequency. Considering the requirements of lock zero accuracy and limitation of the motor torque, the rotational resonant frequency should be from 25 Hz to 50 Hz. Finally, the vibration experiment was carried out. The simulation results are accord with the experimental results, which verifies the correctness of the simulation model.